On Booth lemniscate and starlike functions

Abstract

Assume that ∆ is the open unit disk in the complex plane and A is the class of normalized analytic functions in ∆. In this paper we introduce and study the classwhere 0 ≤ α ≤ 1 and ≺ is the subordination relation. Some properties of this class like differential subordination, coefficients estimates and Fekete-Szegö inequality associated with the k-th root transform are considered.2000 Mathematics Subject Classification. 30C45.

A new subclass of analytic functions

“…Recently, many researchers (see e.g. [1], [6]) have considered the Fekete-Szegö functional associated with the k-th root transform for several subclasses of analytic functions. In the next result, we consider this problem for functions in the class B θ (α, β).…”

Differential subordination and radius estimates for starlike functions associated with the Booth lemniscate

“…The class S * g (φ) of all f ∈ A satisfying z(f (z) * g(z)) ′ /(f (z) * g(z)) ≺ φ(z), where φ(z) is a convex function and g(z) is a fixed function in A, was studied by Shanmugam [31]. For the special case g(z) = z/(1 − z) α , the class S Recently, Kargar et al [10] introduced and studied a class of functions related to the Booth lemniscate.…”

A Study of Third Hankel Determinant Problem for Certain Subfamilies of Analytic Functions Involving Cardioid Domain

“…see also [12,13]. For more special cases of the family S * (φ), see [14,15]. We now consider the following family connected with the cardioid domain:…”